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Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. (English) Zbl 0769.92023
A mathematical model for the transmission dynamics of AIDS epidemics is studied. First, a review of a model for a homosexual population with a single level of epidemiological heterogeneity is given. The properties of this model serve for multiple-group models which are the main subject of the paper. The population is divided into three groups: uninfected people, infected people with mild symptoms and people with AIDS. This model has at most two equilibria, which correspond to the infection-free state and the endemic state. The disease-free equilibrium is globally asymptotically stable if and only if $R\sb 0$, the basic reproductive number, is less or equal to one. If $R\sb 0>1$, there is a unique endemic equilibrium which is locally asymptotically stable. Then, a multiple group model is introduced and the stability of the disease-free equilibrium is studied. The existence and the stability of an endemic equilibrium is studied and a global bifurcation analysis is made to show the existence of multiple endemic equilibria. The relevance of the results is discussed and future directions of research are indicated.

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